Thursday, September 28, 2017

Koide's rule, a formula proposed in 1981, six years after the tau lepton was discovered, when its mass was known much less accurately, predicts the mass of the tau lepton based upon the mass of the electron and the muon. This prediction using current electron and muon mass measurements is:

1776.96894 ± 0.00007 MeV/c^2.

The uncertainty is entirely due to uncertainty in the electron and muon mass measurements. The low uncertainty in the Koide's rule prediction reflects the fact that the electron and muon mass have been measured much more precisely than the tau lepton mass.

This result is 0.06 MeV less than the Koide's rule prediction which is consistent to less than one-half of a standard deviation of experimental uncertainty from the predicted value.

The new result is closer to the Koide's rule prediction than the Particle Data Group (PDG) value for 2016 which is:

1776.83 ± 0.12 MeV/c^2

The PDG value is within about 1.2 standard deviations of the Koide's rule prediction. This new result will probably push the next PDG value closer to the Koide's rule prediction.

Koide's rule is one of the most accurate phenomenological hypotheses in existence which has no Standard Model theoretical explanation, although given the precision to which it is true, there is almost certainly some explanation for this correspondence based upon new physics beyond (or really "within") the Standard Model.

Another Confirmation Of Lepton Universality

The same experiment analyzed its data to determine if it was consistent with lepton universality between tau leptons and muons. The Standard Model predicts lepton universality, but some B meson decay data seem to show weak evidence of a lepton universality violation.

Lepton universality means that all charged leptons have precisely the same properties except mass. The experiment confirmed this prediction of the Standard Model comparing a ratio of two experimental results that should be 1.0 if lepton universality is correct. The measured value of that ratio is:

1.0016 ± 0.0042

Thus, the experimental outcome was again less than half of a standard deviation due to experimental uncertainty from the predicted value and lepton universality is confirmed.